Week 2 : Final Challenge¶
Welcome to the final challenge!
In the previous notebook we've seen how we can use the VQC class in Aqua to classify the digits 0 and 1. However, classifying 0 and 1 is relatively simple as digits 0 and 1 are easily distinguishable. 4 and 9 however, are notoriously similar, with a loop on the top and a line on the bottom. This can be corroborated looking at our 2-D t-SNE plot from the previous notebook (Fig.2), we see that 0 and 1 are clustered relatively far from each other making them easily distinguishable, however 4 and 9 are overlapping. In this challenge we are providing you with a dataset with digits reduced to dimension 3. For example, in Fig.1 we can see the dimension reduction of the 784 dimension vector for digit 4 into a dimension 3 feature vector.
Fig.1 : Features of the digit 4 after reducing dimension to 3:
Fig.2 : MNIST dataset after dimension reduction to 2 as given in the previous notebook:
Challenge Question¶
Use the VQC method from Aqua to classify the digits 4 and 9 as given in the dataset challenge_dataset_4_9_dim3_training.csv provided to you.
Rules and Guidelines¶
- Your
QuantumCircuitcan have a maximum of 6 qubits. - Cost of the circuit should be less than 2000.
- You should not change names of the functions
feature_map(),variational_circuit()andreturn_optimal_params(). - All the functions must return the value types as mentioned.
- All circuits must be Qiskit generated.
- Best of all submissions is considered for grading.
Judging criteria¶
- Primary judgement is based on the accuracy of the model, higher the better. Accuracies which differ by less than 0.005 will be considered to be equal. ex: Accuracies 0.7783 and 0.7741 will be considered to be equal.
- If the accuracies are tied, the tie will be broken using cost of the circuit as the metric, lower the better.
- In the case that both accuracy of the model and cost of the circuit are equal, time of submission is taken into account, Earlier the better.
Important Note: The leaderboard shown during the progress of the competition will only display accuracy of the model and is not the final leaderboard. Breaking ties between accuracy of the model by considering lower cost of circuit will only be done after the competition ends. The final leaderboard will be announced post the event which will take into consideration cost of the circuit and time of submission.
Certificate Eligibility¶
Everyone who scores an accuracy greater than 0.70 (i.e, 70%) will be eligible for a certificate.
An explanation on how to calculate the accuracy of the model and the cost of the circuit is given in the end inside the grade() function. Before you submit, make sure the grading function is running on your device. To save time you can also use the grading function provided to calculate the accuracy and circuit cost without having to submit your solution onto HackerEarth. Remember, your final score will be determined using the same grading methods as given in this notebook, but will be evaluated on unseen datapoints.
In [1]:
# installing a few dependencies
!pip install --upgrade seaborn==0.10.1
!pip install --upgrade scikit-learn==0.23.1
!pip install --upgrade matplotlib==3.2.0
!pip install --upgrade pandas==1.0.4
!pip install --upgrade qiskit==0.19.6
!pip install --upgrade plotly==4.9.0
# the output will be cleared after installation
from IPython.display import clear_output
clear_output()
In [2]:
# we have imported a few libraries we thing might be useful
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit import Aer
from qiskit import *
import numpy as np
from qiskit.visualization import plot_bloch_multivector, plot_histogram
%matplotlib inline
import matplotlib.pyplot as plt
import time
from qiskit.circuit.library import ZZFeatureMap, ZFeatureMap, PauliFeatureMap, RealAmplitudes, EfficientSU2,TwoLocal
from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name
from qiskit.aqua import QuantumInstance
from qiskit.aqua.algorithms import VQC
from qiskit.aqua.components.optimizers import COBYLA
# The the write_and_run() magic function creates a file with the content inside the cell that it is run.
# You have used this in previous exercises for creating your submission files.
# It will be used for the same purpose here.
from IPython.core.magic import register_cell_magic
@register_cell_magic
def write_and_run(line, cell):
argz = line.split()
file = argz[-1]
mode = 'w'
with open(file, mode) as f:
f.write(cell)
get_ipython().run_cell(cell)
Solution¶
Data loading¶
This notebook has helper functions and code snippets to save your time and help you concentrate on what's important: Increasing the accuracy of your model. Running the cell below will import the challenge dataset and will be available to you as data. Before running the cell below store the dataset in this file structure (or change the data_path accordingly):
challenge_notebook.ipynbdatasetchallenge_dataset_4_9.csv
In [3]:
#data_path='./dataset/'
data = np.loadtxt( "challenge_dataset_4_9_dim3_training.csv", delimiter=",")
# extracting the first column which contains the labels
data_labels = data[:, :1].reshape(data.shape[0],)
# extracting all the columns but the first which are our features
data_features = data[:, 1:]
Visualizing the dataset¶
Before we dive into solving the question it is always beneficial to look at the dataset pictographically. This will help us understand patterns which we could leverage when designing our feature maps and variational circuits for example.
In [4]:
import plotly.express as px
import pandas as pd
# creating a dataframe using pandas only for the purpose fo plotting
df = pd.DataFrame({'Component 0':data_features[:,0], 'Component 1':data_features[:,1],
'Component 2':data_features[:,2], 'label':data_labels})
fig = px.scatter_3d(df, x='Component 0', y='Component 1', z='Component 2', color='label')
fig.show()
Extracting the training dataset¶
The given dataset has already been reduced in dimension and normalized, so, further pre-processing isn't techincally required. You can do so if you want to, but the testing dataset will be of the same dimension and normalisation as the training dataset provided. Training a dataset of size 6,000 will take multiple hours so you'll need to extract a subset of the dataset to use as a training dataset. The accuracy of the model may vary based on the datapoints and size of the training dataset you choose. Thus, experimenting with various sizes and datapoints will be necessary. For example, Increasing the training dataset size may increase the accuracy of the model however it will increase the training time as well.
Use the space below to extract your training dataset from data. For your convenience data has been segregated into data_labels and data_features.
data_labels: 6,000 $\times$ 1 column vector with each entry either4or9data_features: 6,000 $\times$ 3 matrix with each row having the feature corresponding to the label indata_labels
Note: This process was done in the previous VQC notebook with 0 and 1 labels and can be modified and used here as well.
Data set¶
We started with training data set of 4000 and soon realized that taling 2000 data point of each points takes too much tme to optemize and shifted to 1500 each. This was a mistake that should never be made.
One must take enough data to train the circuit but not too much that it makes the optemization time taking.
With 2000 data point each it took more then 24 hr for the optemizer to get the minima.
In this file the training has been done with 500 points each and it gives more or less same results.
Lesson to be learned : Take enough points but not too much.¶
In [5]:
### WRITE YOUR CODE BETWEEN THESE LINES - START
# do your classical pre-processing here
#### --------1) seperate data for 9 and 4
four_data_set = []
nine_data_set = []
for i in range(1,6000):
if data_labels[i] == 4: # extracting zeros
four_data_set.append(data_features[i])
for j in range(1, 6000):
if data_labels[j] == 9: # extracting ones
nine_data_set.append(data_features[j])
four_data_set= np.array(four_data_set) # just made it to be an numpy array
nine_data_set= np.array(nine_data_set)
###------2) train and test arrays
train_size = 500
test_size = 500
val = 400
#four_train = []
#nine_train = []
#for i in range (train_size):
# four_train.append((four_data_set[2*i]+four_data_set[2*i+1])/2)
# nine_train.append((nine_data_set[2*i]+nine_data_set[2*i+1])/2)
four_train = four_data_set[:train_size]
nine_train = nine_data_set[:train_size]
four_test = four_data_set[-test_size:]
nine_test = nine_data_set[-test_size:]
four_val = four_data_set[train_size:train_size+val]
nine_val = nine_data_set[train_size:train_size+val]
# store your training and testing datasets to be input in the VQC optimizer in the "training_input" and
# "testing_input" variables respectively. These variables will eb accessed whiile creating a VQC instance later.
training_input = None
testing_input = None
training_input = {'4':four_train, '9':nine_train}
test_input = {'4':four_test, '9':nine_test}
val_input = np.concatenate((four_val,nine_val))
Finding Extra Features¶
Forth Feature¶
Eleminating the third feature we can see that the data set can be seperated by a line or a plane to be exact
In [6]:
import plotly.express as px
import pandas as pd
o = [0]*len(data_features[:,0])
# creating a dataframe using pandas only for the purpose fo plotting
df1 = pd.DataFrame({'Component 0':data_features[:,0], 'Component 1':data_features[:,1],
'Component 2':o, 'label':data_labels})
fig1 = px.scatter_3d(df1, x='Component 0', y='Component 1', z='Component 2', color='label')
fig1.show()
Result¶
The line seperating came up to be of slope m = 1.3.
Now to extract a feature
We need to take the projection of the points to any line perpendicular to the line seperating then so that we can find a point that seperate them in the new feature
Found it to be y = m[x[0],x[1]] = [-1.3,1] [x[0],x[1]] = -1.3x[0]+x[1]
Our new feature is y = -1.3x[0]+x[1]
Fifth Feature¶
If you look the data plot at an angle you will find out that the 9 data is envoloping the 4 data set
In [7]:
fig.show()
In [8]:
a = 0000
b = 6000
z = [0]* len(data_features[a:b,0])
l = [0]* len(data_features[a:b,0])
data_l = data_labels[a:b]
for i in range (len(data_features[a:b,0])):
x = data_features[i,0:3]
z[i] = (0.130554 + 0.087421 *(x[0]**2) + 0.193981* (x[1]**2) + x[0] *(0.14809 - 0.248248 *x[1] - 0.0651 *x[2]) +x[1]*(-0.140875 - 0.0429*x[2]) - 0.319747*x[2] + 0.270152 *(x[2]**2))*10
df2 = pd.DataFrame({'Component 0':z, 'Component 1':l,
'Component 2':l, 'label':data_l})
fig2 = px.scatter_3d(df2, x='Component 0', y='Component 1', z='Component 2', color='label')
fig2.show()
Result¶
You can bairly see the blue outside the confined region.
And the we took the feature to be the distance from the line passing through the center of the blue cylinder like shape
z = (0.130554 + 0.087421 *(x[0]^2) + 0.193981* (x[1]^2) + x[0] *(0.14809 - 0.248248 *x[1] - 0.0651 *x[2]) +x[1]*(-0.140875 - 0.0429*x[2]) - 0.319747*x[2] + 0.270152 *(x[2]^2))*13
We got our 5 features ready to be used [x[0],x[1],x[2],y,z]
Building a Quantum Feature Map¶
Given below is the feature_map() function. It takes no input and has to return a feature map which is either a FeatureMap or QuantumCircuit object. In the previous notebook you've learnt how feature maps work and the process of using existing feature maps in Qiskit or creating your own. In the space given inside the function you have to create a feature map and return it.
IMPORTANT:
- If you require Qiskit import statements other than the ones provided in the cell below, please include them inside the appropriate space provided. All additional import statements must be Qiskit imports.
- the first line of the cell below must be
%%write_and_run feature_map.py. This function stores the content of the cell below in the filefeature_map.py
With the additional 2 new feature we need an custom feature map to use them.¶
We can recreate the default feature mapes with these 2 new features.
Default feature map in qiskit:
- z Feature map
- zz Feature map
- pauli Feature map
With different combinations of map and optimizer we found out that COBYLA is the fastes and it gives best results with ZZ Feature map. So we will try to replicate the ZZ feature map in out custome feature map with 5 features.
In [9]:
%%write_and_run feature_map.py
from qiskit.aqua.components.feature_maps import FeatureMap
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.circuit.library import BlueprintCircuit
import numpy as np
import matplotlib.pyplot as plt
import functools
from qiskit import BasicAer
from qiskit.circuit.library import ZFeatureMap,ZZFeatureMap, PauliFeatureMap
from qiskit.aqua import QuantumInstance
from qiskit.aqua.components.feature_maps import self_product
from qiskit.aqua.algorithms import QSVM
from qiskit.ml.datasets import ad_hoc_data
from numpy import pi
class CustomFeatureMap(FeatureMap):
"""Mapping data with a custom feature map."""
def __init__(self, feature_dimension, depth=2, entangler_map=None):
"""
Args:
feature_dimension (int): number of features
depth (int): the number of repeated circuits
entangler_map (list[list]): describe the connectivity of qubits, each list describes
[source, target], or None for full entanglement.
Note that the order is the list is the order of
applying the two-qubit gate.
"""
self._support_parameterized_circuit = False
self._feature_dimension = feature_dimension
self._num_qubits = self._feature_dimension = feature_dimension+2
self._depth = depth
self._entangler_map = None
if self._entangler_map is None:
self._entangler_map = [[i, j] for i in range(self._feature_dimension) for j in range(i + 1, self._feature_dimension)]
def construct_circuit(self, x, qr, inverse=False):
"""Construct the feature map circuit.
Args:
x (numpy.ndarray): 1-D to-be-transformed data.
qr (QauntumRegister): the QuantumRegister object for the circuit.
inverse (bool): whether or not to invert the circuit.
Returns:
QuantumCircuit: a quantum circuit transforming data x.
"""
qc = QuantumCircuit(5)
for _ in range(self._depth):
y = -1.3*x[0]+x[1]
z = (0.130554 + 0.087421 *(x[0]**2) + 0.193981* (x[1]**2) + x[0] *(0.14809 - 0.248248 *x[1] - 0.0651 *x[2]) +x[1]*(-0.140875 - 0.0429*x[2]) - 0.319747*x[2] + 0.270152 *(x[2]**2))*13
qc.h(0)
qc.h(1)
qc.h(2)
qc.h(3)
qc.u1(x[0],0)
qc.u1(x[1],1)
qc.u1(x[2],2)
qc.u1(y,3)
qc.u1(z,3)
qc.cx(0,1)
qc.u1((2*(pi-x[0])*(pi-x[1])),1)
qc.cx(0,1)
qc.cx(0,2)
qc.u1((2*(pi-x[0])*(pi-x[2])),2)
qc.cx(0,2)
qc.cx(0,3)
qc.u1((2*(pi-x[0])*(pi-y)),3)
qc.cx(0,3)
qc.cx(1,2)
qc.u1((2*(pi-x[1])*(pi-x[2])),2)
qc.cx(1,2)
qc.cx(1,3)
qc.u1((2*(pi-x[1])*(pi-y)),3)
qc.cx(1,3)
qc.cx(2,3)
qc.u1((2*(pi-x[2])*(pi-y)),3)
qc.cx(2,3)
qc.cx(0,4)
qc.u1((2*(pi-x[0])*(pi-z)),4)
qc.cx(0,4)
qc.cx(1,4)
qc.u1((2*(pi-x[1])*(pi-z)),4)
qc.cx(1,4)
qc.cx(2,4)
qc.u1((2*(pi-x[2])*(pi-z)),4)
qc.cx(2,4)
qc.cx(3,4)
qc.u1((2*(pi-y)*(pi-z)),4)
qc.cx(3,4)
if inverse:
qc.inverse()
return qc
def feature_map():
return CustomFeatureMap(feature_dimension=3, depth=2)
Building a Variational Circuit¶
Given below is the variational_circuit() function. It takes no input and has to return a variational circuit which is either a VariationalForm or QuantumCircuit object. In the previous notebook you've learnt how variational circuits work and the process of using existing variational circuit in Qiskit or creating your own. You have to create a variational circuit in the space given inside the function and return it. You can find various variational circuits in the Qiskit Circuit Library under N-local circuits.
IMPORTANT:
- If you require Qiskit import statements other than the ones provided in the cell below, please include them inside the appropriate space provided. All additional import statements must be Qiskit imports.
- the first line of the cell below must be
%%write_and_run feature_map.py. This function stores the content of the cell below in the filevariational_circuit.py
Choosing variotional circuit was quit easy, EfficientSU2 contains all the essential elements to manupulate the state in to give us the best result.
It starts with each qubit manipulation with ry then rz then create entanglment through the cx gate. It gives all the component we needed for an ansatz.
Still we tried the optimization with other Ansatz as well. And with all ESU2 came to be fastest and accurate.
In [10]:
%%write_and_run variational_circuit.py
# the write_and_run function writes the content in this cell into the file "variational_circuit.py"
### WRITE YOUR CODE BETWEEN THESE LINES - START
# import libraries that are used in the function below.
from qiskit import QuantumCircuit
from qiskit.circuit import ParameterVector
from qiskit.circuit.library import RealAmplitudes, EfficientSU2
### WRITE YOUR CODE BETWEEN THESE LINES - END
def variational_circuit():
# BUILD VARIATIONAL CIRCUIT HERE - START
# import required qiskit libraries if additional libraries are required
# build the variational circuit
var_circuit = EfficientSU2(num_qubits=5, su2_gates= ['rx', 'ry'], entanglement='circular', reps=3)
# BUILD VARIATIONAL CIRCUIT HERE - END
return var_circuit
In [ ]:
Choosing a Classical Optimizer¶
In the classical_optimizer() function given below you will have to import the optimizer of your choice from qiskit.aqua.optimizers and return it. This function will not be called by the grading function grade() and thus the name of the function classical_optimizer()can be changed if needed.
Without any compertition COBYLA is the best. Fastest and Accurate of all. Just choose COBYLA.
The tolorance was choosen to be 0.001 which gives enough accuracy to the learning without wasking time for further optemization.
Max_iter is taken to be 1000 so that tolorance can break optemization at the point where it sees fit. Taking lower max iter will stop the optemization in middle way of optemization and the tollorance will never be met.
In [11]:
def classical_optimizer():
# CHOOSE AND RETURN CLASSICAL OPTIMIZER OBJECT - START
# import the required clasical optimizer from qiskit.aqua.optimizers
from qiskit.aqua.components.optimizers import COBYLA
cls_opt = COBYLA(maxiter=1000, tol=0.001)
# CHOOSE AND RETURN CLASSICAL OPTIMIZER OBJECT - END
return cls_opt
Callback Function¶
The VQC class can take in a callback function to which the following parameters will be passed after every optimization cycle of the algorithm:
eval_count: the evaulation countervar_params: value of parameters of the variational circuiteval_val: current cross entropy costindex: the batch index
In [12]:
def call_back_vqc(eval_count, var_params, eval_val, index):
print("eval_count: {}".format(eval_count))
print("var_params: {}".format(var_params))
print("eval_val: {}".format(eval_val))
print("index: {}".format(index))
Optimization Step¶
This is where the whole VQC algorithm will come together. First we create an instance of the VQC class.
With the higher number of shots the chances of error decreases which makes the system more and more ideal as you increase the shots.
We took it to be of scale 10000.
In [13]:
# a fixed seed so that we get the same answer when the same input is given.
seed = 10598
# setting our backend to qasm_simulator with the "statevector" method on. This particular setup is given as it was
# found to perform better than most. Feel free to play around with different backend options.
backend = Aer.get_backend('qasm_simulator')
backend_options = {"method": "statevector"}
# creating a quantum instance using the backend and backend options taken before
quantum_instance = QuantumInstance(backend, shots=10024, seed_simulator=seed, seed_transpiler=seed,
backend_options=backend_options)
# creating a VQC instance which you will be used for training. Make sure you input the correct training_dataset and
# testing_dataset as defined in your program.
vqc = VQC(optimizer=classical_optimizer(),
feature_map=feature_map(),
var_form=variational_circuit(),
callback=call_back_vqc,
training_dataset=training_input, # training_input must be initialized with your training dataset
test_dataset=test_input,datapoints = val_input) # testing_input must be initialized with your testing dataset
c:\users\codie\appdata\local\programs\python\python37\lib\site-packages\qiskit\aqua\algorithms\classifiers\vqc.py:146: DeprecationWarning: The qiskit.aqua.components.feature_maps.FeatureMap object is deprecated as of 0.7.0 and will be removed no earlier than 3 months after the release. You should pass a QuantumCircuit object instead. See also qiskit.circuit.library.data_preparation for a collection of suitable circuits.
Now, let's run the VQC classification routine
In [18]:
start = time.process_time()
result = vqc.run(quantum_instance)
print("time taken: ")
print(time.process_time() - start)
print("testing success ratio: {}".format(result['testing_accuracy']))
eval_count: 0 var_params: [ 0.81552592 -2.04484249 0.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.7341580588035999 index: 0 eval_count: 1 var_params: [ 1.81552592 -2.04484249 0.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.7041316275928419 index: 1 eval_count: 2 var_params: [ 1.81552592 -1.04484249 0.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.6751867827462187 index: 2 eval_count: 3 var_params: [ 1.81552592 -1.04484249 1.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.6892380728836977 index: 3 eval_count: 4 var_params: [ 1.81552592 -1.04484249 0.2008893 -0.13352796 1.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.6968839440465033 index: 4 eval_count: 5 var_params: [ 1.81552592 -1.04484249 0.2008893 -1.13352796 2.12710236 -0.01802996 0.0640288 2.21254166 -2.050838 1.56882253 -0.64204336 -0.07521605 0.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 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eval_count: 25 var_params: [ 1.81552592 -1.04484249 0.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 3.21254166 -2.050838 2.56882253 -0.64204336 0.92478395 1.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -0.01852933 1.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] eval_val: 0.6495633619514399 index: 25 eval_count: 26 var_params: [ 1.81552592 -1.04484249 0.2008893 -1.13352796 1.12710236 -0.01802996 0.0640288 3.21254166 -2.050838 2.56882253 -0.64204336 0.92478395 1.9182025 0.1989012 1.18296009 0.53904314 -0.11945502 0.91771389 -1.99728844 -1.39189883 -1.0048591 -1.11374127 1.48302549 0.69690689 -1.01852933 2.65951077 0.22139255 0.46768721 0.45795897 0.73020292 0.03056902 -0.45874446 0.34333176 -0.75576034 -0.09026524 0.72615639 1.04445187 -0.14296464 0.90181124 -0.47014817] 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-0.22037581] eval_val: 0.4821413912854907 index: 779 eval_count: 780 var_params: [ 0.91844023 -1.08846704 -0.21028076 -0.58196827 1.06963352 -0.04654088 0.59529839 3.54534753 -1.28923553 2.28755173 -1.84479587 0.90887484 2.25372905 -0.4111892 1.67368294 0.3405836 0.92944182 0.20437022 -2.72052649 -1.60109351 -1.50418406 -1.68547731 1.55192245 0.91466348 -1.05618116 0.75416256 0.33064659 0.0977397 0.52812234 0.62633565 0.10553028 -0.01909206 0.36067951 0.96269394 0.79415579 2.07247274 0.10732682 0.00977323 0.38164168 -0.22056278] eval_val: 0.4821746544650546 index: 780 eval_count: 781 var_params: [ 0.91819861 -1.08803061 -0.21034761 -0.58220239 1.06948539 -0.04655229 0.59532506 3.54529501 -1.28937565 2.28753513 -1.84487627 0.90878965 2.25382327 -0.4112682 1.67356742 0.34080654 0.92952939 0.20456005 -2.72046907 -1.60109636 -1.50452226 -1.68566927 1.55196172 0.91478943 -1.05627482 0.75408732 0.3305201 0.09761095 0.52820615 0.62623902 0.10557911 -0.01882213 0.36084601 0.96292259 0.79426497 2.0724149 0.10716824 0.00991753 0.38122294 -0.22019716] eval_val: 0.48216041676338345 index: 781 eval_count: 782 var_params: [ 0.91841666 -1.08815206 -0.21049422 -0.58212349 1.06935608 -0.04636033 0.59565343 3.54531493 -1.28948598 2.2876312 -1.84509938 0.90900078 2.2537377 -0.41161765 1.67354679 0.34068803 0.92982044 0.20460006 -2.72078244 -1.60102516 -1.50441094 -1.68558165 1.55173864 0.9149476 -1.05645803 0.75395183 0.3304938 0.0974527 0.52825799 0.62632833 0.105404 -0.01903291 0.36104412 0.96263254 0.79430746 2.07275597 0.10717517 0.00962181 0.38124171 -0.22023409] eval_val: 0.4821597188927806 index: 782 eval_count: 783 var_params: [ 0.91839589 -1.08793845 -0.21043128 -0.58209953 1.06942572 -0.0463714 0.59532363 3.5453597 -1.28912158 2.28747646 -1.84475656 0.90890565 2.253824 -0.41135835 1.67357134 0.34071174 0.92958333 0.20455054 -2.72059014 -1.60107143 -1.50460245 -1.68572925 1.55188668 0.91482343 -1.05628359 0.75414943 0.33046546 0.0977061 0.52831649 0.62613972 0.10563414 -0.01906901 0.36079659 0.96276193 0.79425046 2.07246517 0.10727927 0.00983904 0.38111799 -0.22048708] eval_val: 0.4821472877452445 index: 783 eval_count: 784 var_params: [ 0.9182993 -1.08833632 -0.21027117 -0.58211283 1.06914482 -0.04657307 0.59525426 3.5452801 -1.28908915 2.28758615 -1.84478563 0.90878194 2.25394318 -0.41109871 1.67347314 0.34058035 0.92976736 0.20455985 -2.72086562 -1.60081113 -1.50468495 -1.68575863 1.55186646 0.91481398 -1.05637275 0.7543963 0.33028529 0.09754041 0.52828585 0.62592169 0.10557304 -0.01900788 0.36100456 0.96271653 0.79440196 2.07246548 0.10721031 0.01009141 0.38154017 -0.2201163 ] eval_val: 0.482153984972455 index: 784 eval_count: 785 var_params: [ 0.9183759 -1.08812969 -0.21031671 -0.58210331 1.06945795 -0.04641724 0.59547044 3.54520705 -1.2892666 2.28763942 -1.84479804 0.9088698 2.25385793 -0.41131323 1.673486 0.34072038 0.92978305 0.2046592 -2.7206377 -1.60103625 -1.50460145 -1.68556567 1.55194713 0.91497507 -1.05614556 0.75406646 0.33066284 0.09765191 0.528313 0.62619396 0.10567473 -0.01891994 0.36087907 0.96282014 0.7941664 2.07221006 0.10731818 0.00989824 0.38130128 -0.22035845] eval_val: 0.48214968720497875 index: 785 eval_count: 786 var_params: [ 0.91841551 -1.08780264 -0.2103359 -0.58229807 1.06962724 -0.04672907 0.59562757 3.54506511 -1.28926036 2.28766913 -1.84469743 0.90879162 2.25382499 -0.41131075 1.67357473 0.3406828 0.9295354 0.20472005 -2.72056269 -1.60070021 -1.50446086 -1.68544488 1.55186204 0.91501608 -1.05644187 0.75429372 0.33041609 0.09783927 0.52798554 0.62602403 0.10591374 -0.0188937 0.36094087 0.96258245 0.7940191 2.07257757 0.10702935 0.00988337 0.38128369 -0.22047478] eval_val: 0.4821488438232726 index: 786 eval_count: 787 var_params: [ 0.91854302 -1.08798177 -0.21009535 -0.58232799 1.06935428 -0.04641256 0.59552509 3.54519991 -1.28918848 2.28766243 -1.84491546 0.90895254 2.2535594 -0.41148327 1.6737878 0.34052944 0.92970678 0.20448063 -2.72046037 -1.60088967 -1.50488751 -1.68597962 1.55208916 0.9146031 -1.05649925 0.75403961 0.33066391 0.09772049 0.5280793 0.62611578 0.1055327 -0.0188807 0.36066003 0.96266194 0.79398824 2.0723008 0.10734654 0.00983166 0.38139291 -0.22015975] eval_val: 0.4821559820490442 index: 787 time taken: 46831.546875 testing success ratio: 0.8
Storing the optimal parameters for grading¶
Once the training step of the vqc algorithm is done we obtain the optimal parameters for our specific variational form. For the grading function to be able to access these optimal parameters you will need to follow the steps below.
- Step 1: Run the cell below with
print(repr(vqc.optimal_params)). - Step 2: Copy the matrix of optimal parameters and store it in the variable
optimal_parametersinside the functionreturn_optimal_params()in the next cell. This will enable us to extract it while calculating the accuracy your the model during grading. Given below is a pictographical explanation of the same:
In [19]:
print(repr(vqc.optimal_params))
array([ 0.91854302, -1.08798177, -0.21009535, -0.58232799, 1.06935428,
-0.04641256, 0.59552509, 3.54519991, -1.28918848, 2.28766243,
-1.84491546, 0.90895254, 2.2535594 , -0.41148327, 1.6737878 ,
0.34052944, 0.92970678, 0.20448063, -2.72046037, -1.60088967,
-1.50488751, -1.68597962, 1.55208916, 0.9146031 , -1.05649925,
0.75403961, 0.33066391, 0.09772049, 0.5280793 , 0.62611578,
0.1055327 , -0.0188807 , 0.36066003, 0.96266194, 0.79398824,
2.0723008 , 0.10734654, 0.00983166, 0.38139291, -0.22015975])
In [14]:
%%write_and_run optimal_params.py
# # the write_and_run function writes the content in this cell into the file "optimal_params.py"
### WRITE YOUR CODE BETWEEN THESE LINES - START
# import libraries that are used in the function below.
import numpy as np
### WRITE YOUR CODE BETWEEN THESE LINES - END
def return_optimal_params():
# STORE THE OPTIMAL PARAMETERS AS AN ARRAY IN THE VARIABLE optimal_parameters
optimal_parameters =[ 0.91854302, -1.08798177, -0.21009535, -0.58232799, 1.06935428,
-0.04641256, 0.59552509, 3.54519991, -1.28918848, 2.28766243,
-1.84491546, 0.90895254, 2.2535594 , -0.41148327, 1.6737878 ,
0.34052944, 0.92970678, 0.20448063, -2.72046037, -1.60088967,
-1.50488751, -1.68597962, 1.55208916, 0.9146031 , -1.05649925,
0.75403961, 0.33066391, 0.09772049, 0.5280793 , 0.62611578,
0.1055327 , -0.0188807 , 0.36066003, 0.96266194, 0.79398824,
2.0723008 , 0.10734654, 0.00983166, 0.38139291, -0.22015975]
# STORE THE OPTIMAL PARAMETERS AS AN ARRAY IN THE VARIABLE optimal_parameters
return np.array(optimal_parameters)
Submission¶
Before we go any further, check that you have the three files feature_map.py, variational_circuit.py and optimal_params.py in the same working directory as this notebook. If you do not, then go back to the start and run the notebook making sure you have filled in the code where its required. When you run the cell below, all the three files feature_map.py, variational_circuit.py and optimal_params.py are combined into one file named "answer.py". Now your working directory will have four python (.py) files out of which "answer.py" is the submission file:
answer.py<- upload this file onto HackerEarth and click on "Submit and Evaluate"feature_map.pyvariational_circuit.pyoptimal_params.py
In [15]:
solution = ['feature_map.py','variational_circuit.py','optimal_params.py']
file = open("answer.py","w")
file.truncate(0)
for i in solution:
with open(i) as f:
with open("answer.py", "a") as f1:
for line in f:
f1.write(line)
file.close()
Grading Function¶
Given below is the grading function that we shall use to grade your submission with a test dataset that is of the same format as challenge_dataset_4_9.csv. You can use it to grade your submission by extracting a few points out of the challenge_dataset_4_9.csv to get a basic idea of how your model is performing.
In [16]:
#imports required for the grading function
from qiskit import *
from qiskit.aqua import QuantumInstance
from qiskit.aqua.algorithms import VQC
from qiskit.aqua.components.feature_maps import FeatureMap
from qiskit.aqua.components.variational_forms import VariationalForm
import numpy as np
Working of the grading function¶
The grading function grade() takes as input:
test_data: (np.ndarray) -- no. of datapoints $\times$ dimension of data : the datapoints against which we want to test our model.
test_labels: (np.ndarray) -- no. of datapoints $\times$ 1 : A column vector with each entry either 0 or 1 as entries.
feature_map: (QuantumCircuitorFeatureMap) -- A quantum feature map which is the output offeature_map()defined earlier.
variational_form: (QuantumCircuitorVariationalForm) -- A variational form which is the output ofvariational_circuit()defined earlier.
optimal_params: (numpy.ndarray) -- the optimal parameters obtained after running the VQC algorithm above. These are the values obtained when the functionreturn_optimal_params()is run.
find_circuit_cost: (bool) -- Calculates the circuit cost if set toTrue. Circuit cost is calculated by converting the circuit to the basis gate set\[ 'u3', 'cx'\]and then applying the formula cost = 1$\times$(no.of u3 gates) + 10$\times$(no.of cx gates).
verbose: (bool) -- prints the result message if set toTrue.
And gives as output:
model_accuracy: (numpy.float64) -- percent accuracy of the model.
circuit_cost: (int) -- circuit cost as explained above.
ans: (tuple) -- Output of theVQC.predict()method.
result_msg: (str) -- Result message which also outputs the error message in case of one.
unrolled_circuit: (QuantumCircuitorNone) -- the circuit obtained after unrolling the full VQC circuit and substituting the optimal parameters to the basis gate set\[ 'u3', 'cx'\].
Note: if you look inside the grade() function in Section 2 you'll see that we have initialized a COBYLA optimizer though the prediction step will not require one. Similarily we have given a dataset to training dataset. Both of these are dummy variables. The reason for this is because these are not optional variables the VQC class instantiation.
In [17]:
def grade(test_data, test_labels, feature_map, variational_form, optimal_params, find_circuit_cost=True, verbose=True):
seed = 10598
model_accuracy = None
circuit_cost=None
ans = None
unrolled_circuit = None
result_msg=''
data_dim = np.array(test_data).shape[1]
dataset_size = np.array(test_data).shape[0]
dummy_training_dataset=training_input = {'A':np.ones((2,data_dim)), 'B':np.ones((2, data_dim))}
# converting 4's to 0's and 9's to 1's for checking
test_labels_transformed = np.where(test_labels==4, 0., 1.)
max_qubit_count = 6
max_circuit_cost = 2000
# Section 1
if feature_map is None:
result_msg += 'feature_map variable is None. Please submit a valid entry' if verbose else ''
elif variational_form is None:
result_msg += 'variational_form variable is None. Please submit a valid entry' if verbose else ''
elif optimal_params is None:
result_msg += 'optimal_params variable is None. Please submit a valid entry' if verbose else ''
elif test_data is None:
result_msg += 'test_data variable is None. Please submit a valid entry' if verbose else ''
elif test_labels is None:
result_msg += 'test_labels variable is None. Please submit a valid entry' if verbose else ''
elif not isinstance(feature_map, (QuantumCircuit, FeatureMap)):
result_msg += 'feature_map variable should be a QuantumCircuit or a FeatureMap not (%s)' % \
type(feature_map) if verbose else ''
elif not isinstance(variational_form, (QuantumCircuit, VariationalForm)):
result_msg += 'variational_form variable should be a QuantumCircuit or a VariationalForm not (%s)' % \
type(variational_form) if verbose else ''
elif not isinstance(test_data, np.ndarray):
result_msg += 'test_data variable should be a numpy.ndarray not (%s)' % \
type(test_data) if verbose else ''
elif not isinstance(test_labels, np.ndarray):
result_msg += 'test_labels variable should be a numpy.ndarray not (%s)' % \
type(test_labels) if verbose else ''
elif not isinstance(optimal_params, np.ndarray):
result_msg += 'optimal_params variable should be a numpy.ndarray not (%s)' % \
type(optimal_params) if verbose else ''
elif not dataset_size == test_labels_transformed.shape[0]:
result_msg += 'Dataset size and label array size must be equal'
# Section 2
else:
# setting up COBYLA optimizer as a dummy optimizer
from qiskit.aqua.components.optimizers import COBYLA
dummy_optimizer = COBYLA()
# setting up the backend and creating a quantum instance
backend = Aer.get_backend('qasm_simulator')
backend_options = {"method": "statevector"}
quantum_instance = QuantumInstance(backend,
shots=2000,
seed_simulator=seed,
seed_transpiler=seed,
backend_options=backend_options)
# creating a VQC instance and running the VQC.predict method to get the accuracy of the model
vqc = VQC(optimizer=dummy_optimizer,
feature_map=feature_map,
var_form=variational_form,
training_dataset=dummy_training_dataset)
from qiskit.transpiler import PassManager
from qiskit.transpiler.passes import Unroller
pass_ = Unroller(['u3', 'cx'])
pm = PassManager(pass_)
# construct circuit with first datapoint
circuit = vqc.construct_circuit(data[0], optimal_params)
unrolled_circuit = pm.run(circuit)
gates = unrolled_circuit.count_ops()
if 'u3' in gates:
circuit_cost = gates['u3']
if 'cx' in gates:
circuit_cost+= 10*gates['cx']
if circuit.num_qubits > max_qubit_count:
result_msg += 'Your quantum circuit is using more than 6 qubits. Reduce the number of qubits used and try again.'
elif circuit_cost > max_circuit_cost:
result_msg += 'The cost of your circuit is exceeding the maximum accpetable cost of 2000. Reduce the circuit cost and try again.'
else:
ans = vqc.predict(test_data, quantum_instance=quantum_instance, params=np.array(optimal_params))
model_accuracy = np.sum(np.equal(test_labels_transformed, ans[1]))/len(ans[1])
result_msg += 'Accuracy of the model is {}'.format(model_accuracy) if verbose else ''
result_msg += ' and circuit cost is {}'.format(circuit_cost) if verbose else ''
return model_accuracy, circuit_cost, ans, result_msg, unrolled_circuit
Process of grading using a dummy grading dataset¶
Let us create a dummy grading dataset with features and labels grading_features and grading_labels created from the last 2000 datapoints from data_features and data_labelsso that we can a rough estimate of our accuaracy. It must be noted that this may not be a balanced dataset, i.e, may not have equal number of 4's and 9's and is not best practice. This is only given for the purpose of the demo of grade() function. In the final scoring done on HackerEarth, the testing dataset used will have a balanced number of class labels 4 and 9.
In [20]:
grading_dataset_size=4000 # this value is not per digit but in total
grading_features = data_features[-grading_dataset_size:]
grading_labels = data_labels[-grading_dataset_size:]
In [21]:
start = time.process_time()
accuracy, circuit_cost, ans, result_msg, full_circuit = grade(test_data=grading_features,
test_labels=grading_labels,
feature_map=feature_map(),
variational_form=variational_circuit(),
optimal_params=return_optimal_params())
print("time taken: {} seconds".format(time.process_time() - start))
print(result_msg)
c:\users\codie\appdata\local\programs\python\python37\lib\site-packages\qiskit\aqua\algorithms\classifiers\vqc.py:146: DeprecationWarning: The qiskit.aqua.components.feature_maps.FeatureMap object is deprecated as of 0.7.0 and will be removed no earlier than 3 months after the release. You should pass a QuantumCircuit object instead. See also qiskit.circuit.library.data_preparation for a collection of suitable circuits.
time taken: 180.65625 seconds Accuracy of the model is 0.8065 and circuit cost is 628
You can also check your accuracy, circuit_cost and full_circuit which is the result of combining the feature map and variational circuit and unrolling into the basis ['u3', 'cx'].
In [29]:
print("Accuracy of the model: {}".format(accuracy))
print("Circuit Cost: {}".format(circuit_cost))
print("The complete unrolled circuit: ")
full_circuit.draw()
Accuracy of the model: 0.80625 Circuit Cost: 628 The complete unrolled circuit:
Out[29]:
┌───────────────┐ ┌───────────┐ »
q_0: ┤ U3(pi/2,0,pi) ├───┤ U3(0,0,4) ├───────────■────────────────────────────»
├───────────────┤ ┌─┴───────────┴──┐ ┌─┴─┐ ┌─────────────────┐»
q_1: ┤ U3(pi/2,0,pi) ├─┤ U3(0,0,0.8228) ├──────┤ X ├───────┤ U3(0,0,-3.9809) ├»
├───────────────┤┌┴────────────────┤ └───┘ └─────────────────┘»
q_2: ┤ U3(pi/2,0,pi) ├┤ U3(0,0,0.90163) ├─────────────────────────────────────»
├───────────────┤├─────────────────┤┌────────────────┐ »
q_3: ┤ U3(pi/2,0,pi) ├┤ U3(0,0,-4.3772) ├┤ U3(0,0,12.802) ├───────────────────»
└───────────────┘└─────────────────┘└────────────────┘ »
q_4: ─────────────────────────────────────────────────────────────────────────»
»
c_0: ═════════════════════════════════════════════════════════════════════════»
»
c_1: ═════════════════════════════════════════════════════════════════════════»
»
c_2: ═════════════════════════════════════════════════════════════════════════»
»
c_3: ═════════════════════════════════════════════════════════════════════════»
»
c_4: ═════════════════════════════════════════════════════════════════════════»
»
« »
«q_0: ──■────■───────────────────────■─────────■────────────────────────────■──»
« ┌─┴─┐ │ │ │ │ »
«q_1: ┤ X ├──┼───────────────────────┼────■────┼───────────────────────■────┼──»
« └───┘┌─┴─┐┌─────────────────┐┌─┴─┐┌─┴─┐ │ ┌────────────────┐┌─┴─┐ │ »
«q_2: ─────┤ X ├┤ U3(0,0,-3.8456) ├┤ X ├┤ X ├──┼───┤ U3(0,0,10.388) ├┤ X ├──┼──»
« └───┘└─────────────────┘└───┘└───┘┌─┴─┐┌┴────────────────┤└───┘┌─┴─┐»
«q_3: ───────────────────────────────────────┤ X ├┤ U3(0,0,-12.908) ├─────┤ X ├»
« └───┘└─────────────────┘ └───┘»
«q_4: ─────────────────────────────────────────────────────────────────────────»
« »
«c_0: ═════════════════════════════════════════════════════════════════════════»
« »
«c_1: ═════════════════════════════════════════════════════════════════════════»
« »
«c_2: ═════════════════════════════════════════════════════════════════════════»
« »
«c_3: ═════════════════════════════════════════════════════════════════════════»
« »
«c_4: ═════════════════════════════════════════════════════════════════════════»
« »
« ┌───────────────┐┌───────────┐»
«q_0: ───────■───────────────────────────■──┤ U3(pi/2,0,pi) ├┤ U3(0,0,4) ├»
« │ │ └───────────────┘└───────────┘»
«q_1: ──■────┼──────────────────────■────┼─────────────────────────■──────»
« │ │ │ │ │ »
«q_2: ──┼────┼──────────────────────┼────┼──────────■──────────────┼──────»
« ┌─┴─┐ │ ┌────────────────┐┌─┴─┐ │ ┌─┴─┐ │ »
«q_3: ┤ X ├──┼──┤ U3(0,0,34.869) ├┤ X ├──┼────────┤ X ├────────────┼──────»
« └───┘┌─┴─┐├────────────────┤└───┘┌─┴─┐ └───┘ ┌─┴─┐ »
«q_4: ─────┤ X ├┤ U3(0,0,16.584) ├─────┤ X ├─────────────────────┤ X ├────»
« └───┘└────────────────┘ └───┘ └───┘ »
«c_0: ════════════════════════════════════════════════════════════════════»
« »
«c_1: ════════════════════════════════════════════════════════════════════»
« »
«c_2: ════════════════════════════════════════════════════════════════════»
« »
«c_3: ════════════════════════════════════════════════════════════════════»
« »
«c_4: ════════════════════════════════════════════════════════════════════»
« »
« »
«q_0: ───────────────────────────────────────────────────────────────────■──»
« ┌───────────────┐ ┌────────────────┐┌─┴─┐»
«q_1: ──────────────────────────■──┤ U3(pi/2,0,pi) ├─┤ U3(0,0,0.8228) ├┤ X ├»
« │ └───────────────┘ └────────────────┘└───┘»
«q_2: ─────────────────────■────┼──────────■─────────────────────────────■──»
« ┌────────────────┐┌─┴─┐ │ │ │ »
«q_3: ─┤ U3(0,0,33.684) ├┤ X ├──┼──────────┼─────────────────────────────┼──»
« ┌┴────────────────┤└───┘┌─┴─┐ ┌─┴─┐ ┌─────────────────┐┌─┴─┐»
«q_4: ┤ U3(0,0,-44.799) ├─────┤ X ├──────┤ X ├──────┤ U3(0,0,-43.276) ├┤ X ├»
« └─────────────────┘ └───┘ └───┘ └─────────────────┘└───┘»
«c_0: ══════════════════════════════════════════════════════════════════════»
« »
«c_1: ══════════════════════════════════════════════════════════════════════»
« »
«c_2: ══════════════════════════════════════════════════════════════════════»
« »
«c_3: ══════════════════════════════════════════════════════════════════════»
« »
«c_4: ══════════════════════════════════════════════════════════════════════»
« »
« »
«q_0: ────────────────────────────■───────────■─────────────────────»
« ┌─────────────────┐ ┌─┴─┐ │ »
«q_1: ┤ U3(0,0,-3.9809) ├───────┤ X ├─────────┼─────────────────────»
« └┬───────────────┬┘┌──────┴───┴──────┐┌─┴─┐┌─────────────────┐»
«q_2: ─┤ U3(pi/2,0,pi) ├─┤ U3(0,0,0.90163) ├┤ X ├┤ U3(0,0,-3.8456) ├»
« └───────────────┘ └─────────────────┘└───┘└┬───────────────┬┘»
«q_3: ─────────■──────────────────────────────■───┤ U3(pi/2,0,pi) ├─»
« ┌─┴─┐ ┌─────────────────┐┌─┴─┐ └───────────────┘ »
«q_4: ───────┤ X ├───────┤ U3(0,0,-145.26) ├┤ X ├───────────────────»
« └───┘ └─────────────────┘└───┘ »
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«q_0: ─────────■───────────────────────────────────────────────■──»
« │ │ »
«q_1: ─────────┼─────────────────■─────────────────────────────┼──»
« ┌─┴─┐ ┌─┴─┐ ┌────────────────┐ │ »
«q_2: ───────┤ X ├─────────────┤ X ├───────┤ U3(0,0,10.388) ├──┼──»
« ┌──────┴───┴──────┐┌─────┴───┴──────┐└────────────────┘┌─┴─┐»
«q_3: ┤ U3(0,0,-4.3772) ├┤ U3(0,0,12.802) ├──────────────────┤ X ├»
« └─────────────────┘└────────────────┘ └───┘»
«q_4: ────────────────────────────────────────────────────────────»
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«c_0: ════════════════════════════════════════════════════════════»
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«q_0: ─────────────────────■────■───────────────────────────────────────────»
« │ │ »
«q_1: ─────────■───────────┼────┼──────────■─────────────────────────────■──»
« ┌─┴─┐ │ │ │ │ »
«q_2: ───────┤ X ├─────────┼────┼──────────┼─────────────────────────────┼──»
« ┌──────┴───┴──────┐┌─┴─┐ │ ┌─┴─┐ ┌────────────────┐┌─┴─┐»
«q_3: ┤ U3(0,0,-12.908) ├┤ X ├──┼────────┤ X ├───────┤ U3(0,0,34.869) ├┤ X ├»
« └─────────────────┘└───┘┌─┴─┐┌─────┴───┴──────┐└────────────────┘└───┘»
«q_4: ────────────────────────┤ X ├┤ U3(0,0,16.584) ├───────────────────────»
« └───┘└────────────────┘ »
«c_0: ══════════════════════════════════════════════════════════════════════»
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« ┌────────────────────────┐┌────────────────┐ »
«q_0: ──■──┤ U3(0.91854,-pi/2,pi/2) ├┤ U3(2.0723,0,0) ├────────────────────────»
« │ └────────────────────────┘└────────────────┘ »
«q_1: ──┼────────────────────────────────────■─────────────────────────────────»
« │ │ »
«q_2: ──┼──────────────■─────────────────────┼──────────────────────────────■──»
« │ ┌─┴─┐ │ ┌────────────────┐┌─┴─┐»
«q_3: ──┼────────────┤ X ├───────────────────┼──────────┤ U3(0,0,33.684) ├┤ X ├»
« ┌─┴─┐ └───┘ ┌─┴─┐ ┌┴────────────────┤└───┘»
«q_4: ┤ X ├────────────────────────────────┤ X ├───────┤ U3(0,0,-44.799) ├─────»
« └───┘ └───┘ └─────────────────┘ »
«c_0: ═════════════════════════════════════════════════════════════════════════»
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«c_1: ═════════════════════════════════════════════════════════════════════════»
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« »
«q_0: ───────────────────────────────────────────────────────»
« ┌────────────────────────┐┌─────────────────┐ »
«q_1: ──■──┤ U3(0.90895,-pi/2,pi/2) ├┤ U3(0.10735,0,0) ├─────»
« │ └────────────────────────┘└─────────────────┘ »
«q_2: ──┼──────────────■──────────────────────────────────■──»
« │ │ │ »
«q_3: ──┼──────────────┼──────────────────────────────────┼──»
« ┌─┴─┐ ┌─┴─┐ ┌─────────────────┐┌─┴─┐»
«q_4: ┤ X ├──────────┤ X ├───────────┤ U3(0,0,-43.276) ├┤ X ├»
« └───┘ └───┘ └─────────────────┘└───┘»
«c_0: ═══════════════════════════════════════════════════════»
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«q_0: ───────────────────────────────────────────────────»
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«q_1: ───────────────────────────────────────────────────»
« ┌───────────────────────┐┌───────────────────┐ »
«q_2: ┤ U3(1.5521,-pi/2,pi/2) ├┤ U3(0.0098317,0,0) ├─────»
« └───────────────────────┘└───────────────────┘ »
«q_3: ────────────■───────────────────────────────────■──»
« ┌─┴─┐ ┌─────────────────┐ ┌─┴─┐»
«q_4: ──────────┤ X ├───────────┤ U3(0,0,-145.26) ├─┤ X ├»
« └───┘ └─────────────────┘ └───┘»
«c_0: ═══════════════════════════════════════════════════»
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« ┌───┐ »
«q_0: ──────────────────────────────────────────────┤ X ├──■──»
« └─┬─┘┌─┴─┐»
«q_1: ────────────────────────────────────────────────┼──┤ X ├»
« │ └───┘»
«q_2: ────────────────────────────────────────────────┼───────»
« ┌────────────────────────┐┌─────────────────┐ │ »
«q_3: ┤ U3(0.96266,-pi/2,pi/2) ├┤ U3(0.38139,0,0) ├───┼───────»
« ├────────────────────────┤├─────────────────┴┐ │ »
«q_4: ┤ U3(0.79399,-pi/2,pi/2) ├┤ U3(-0.22016,0,0) ├──■───────»
« └────────────────────────┘└──────────────────┘ »
«c_0: ════════════════════════════════════════════════════════»
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« ┌───────────────────────┐ ┌─────────────────┐ »
«q_0: ┤ U3(-1.088,-pi/2,pi/2) ├───┤ U3(0.59553,0,0) ├────»
« └───────────────────────┘┌──┴─────────────────┴───┐»
«q_1: ────────────■────────────┤ U3(-0.2101,-pi/2,pi/2) ├»
« ┌─┴─┐ └────────────────────────┘»
«q_2: ──────────┤ X ├──────────────────────■─────────────»
« └───┘ ┌─┴─┐ »
«q_3: ───────────────────────────────────┤ X ├───────────»
« └───┘ »
«q_4: ───────────────────────────────────────────────────»
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«q_0: ───────────────────────────────────────────────────────»
« ┌────────────────┐ »
«q_1: ─────┤ U3(3.5452,0,0) ├────────────────────────────────»
« ┌────┴────────────────┴───┐ ┌─────────────────┐ »
«q_2: ┤ U3(-0.58233,-pi/2,pi/2) ├────┤ U3(-1.2892,0,0) ├─────»
« └─────────────────────────┘ ┌──┴─────────────────┴──┐ »
«q_3: ─────────────■──────────────┤ U3(1.0694,-pi/2,pi/2) ├──»
« ┌─┴─┐ ┌┴───────────────────────┴─┐»
«q_4: ───────────┤ X ├───────────┤ U3(-0.046413,-pi/2,pi/2) ├»
« └───┘ └──────────────────────────┘»
«c_0: ═══════════════════════════════════════════════════════»
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« ┌───┐ ┌───────────────────────┐»
«q_0: ───────────────────┤ X ├──■──┤ U3(2.2536,-pi/2,pi/2) ├»
« └─┬─┘┌─┴─┐└───────────────────────┘»
«q_1: ─────────────────────┼──┤ X ├────────────■────────────»
« │ └───┘ ┌─┴─┐ »
«q_2: ─────────────────────┼─────────────────┤ X ├──────────»
« ┌────────────────┐ │ └───┘ »
«q_3: ─┤ U3(2.2877,0,0) ├──┼────────────────────────────────»
« ┌┴────────────────┤ │ »
«q_4: ┤ U3(-1.8449,0,0) ├──■────────────────────────────────»
« └─────────────────┘ »
«c_0: ══════════════════════════════════════════════════════»
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« ┌─────────────────┐ »
«q_0: ────┤ U3(0.20448,0,0) ├─────────────────────────────»
« ┌───┴─────────────────┴───┐ ┌─────────────────┐ »
«q_1: ┤ U3(-0.41148,-pi/2,pi/2) ├───┤ U3(-2.7205,0,0) ├───»
« └─────────────────────────┘┌──┴─────────────────┴──┐»
«q_2: ─────────────■─────────────┤ U3(1.6738,-pi/2,pi/2) ├»
« ┌─┴─┐ └───────────────────────┘»
«q_3: ───────────┤ X ├───────────────────────■────────────»
« └───┘ ┌─┴─┐ »
«q_4: ─────────────────────────────────────┤ X ├──────────»
« └───┘ »
«c_0: ════════════════════════════════════════════════════»
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« ┌───┐ »
«q_0: ─────────────────────────────────────────────┤ X ├──■──»
« └─┬─┘┌─┴─┐»
«q_1: ───────────────────────────────────────────────┼──┤ X ├»
« ┌─────────────────┐ │ └───┘»
«q_2: ───┤ U3(-1.6009,0,0) ├─────────────────────────┼───────»
« ┌──┴─────────────────┴───┐┌─────────────────┐ │ »
«q_3: ┤ U3(0.34053,-pi/2,pi/2) ├┤ U3(-1.5049,0,0) ├──┼───────»
« ├────────────────────────┤└┬────────────────┤ │ »
«q_4: ┤ U3(0.92971,-pi/2,pi/2) ├─┤ U3(-1.686,0,0) ├──■───────»
« └────────────────────────┘ └────────────────┘ »
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« ┌───────────────────────┐ ┌─────────────────┐ »
«q_0: ┤ U3(0.9146,-pi/2,pi/2) ├───┤ U3(0.52808,0,0) ├────»
« └───────────────────────┘┌──┴─────────────────┴───┐»
«q_1: ────────────■────────────┤ U3(-1.0565,-pi/2,pi/2) ├»
« ┌─┴─┐ └────────────────────────┘»
«q_2: ──────────┤ X ├──────────────────────■─────────────»
« └───┘ ┌─┴─┐ »
«q_3: ───────────────────────────────────┤ X ├───────────»
« └───┘ »
«q_4: ───────────────────────────────────────────────────»
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«
«q_0: ─────────────────────────────────────────────────────────────────────────
« ┌─────────────────┐
«q_1: ───┤ U3(0.62612,0,0) ├───────────────────────────────────────────────────
« ┌──┴─────────────────┴───┐ ┌─────────────────┐
«q_2: ┤ U3(0.75404,-pi/2,pi/2) ├───┤ U3(0.10553,0,0) ├─────────────────────────
« └────────────────────────┘┌──┴─────────────────┴───┐┌───────────────────┐
«q_3: ────────────■─────────────┤ U3(0.33066,-pi/2,pi/2) ├┤ U3(-0.018881,0,0) ├
« ┌─┴─┐ ├────────────────────────┤└┬─────────────────┬┘
«q_4: ──────────┤ X ├───────────┤ U3(0.09772,-pi/2,pi/2) ├─┤ U3(0.36066,0,0) ├─
« └───┘ └────────────────────────┘ └─────────────────┘
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Accuracy¶
Accuracy was found to be 0.806 which can give 0.806+-0.01 accuracy on the online server. More preferebely +0.01 as other circuits gave.
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